Let $k$ be a field, and define $R=k[x,y]$.
I'm supposed to find two different **minimal **primary decompositions of the ideal $(x^2y, y^2x)$.
It's easy to see that one minimal primary decomposition is $(x), (y), (x^2, y^2)$.
My question: What's the second *minimal * primary decomposition of the above ideal?
EDIT: I've now added the minimality requirement to the question.